Such a blow molding machine is known from EP 1 328 396. In the known blow molding machine, the relative movement between the blow nozzle and the blow mold which is required for introducing the preform into the blow mold and for blowing is achieved by a merely mechanical drive of the vertical movement. The mechanical drive contains a cam roller which, in connection with a radial cam, defines the vertical movement and the position of the blow nozzle. The cam roller is associated to the blow nozzle and the radial cam to the blow mold, so that by the usual relative rotation about a vertical axis of the blow mold and the blow nozzle, the vertical movement is derived from the drive of the rotary motion. A disadvantage of this embodiment is the lack of flexibility of the drive as the radial cam is fixed locally and with respect to the dimension of the movement.